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After a thread on the forums about aimtime and how it works. I decided I wanted to figure it out exactly. All we know for now is that aim time is the time it take to reduce the aimcircle to 40% its size, dispersion is something that say show much the circle gets bigger and accuracy is the size of the aimingcircle when fully aimed. However, we do not know the exact relations between these 2 and how exactly they influence the size of the aiming circle at all times. So thats what I set out to do, finding a mathmatical description of the size of the aimingcircle. The method is simple: measure the size of the aimingcircle for different tanks and speeds in a trainingroom. Thanks for uglycousin for giving me a second person to set up the trainingroom. To measure the size of the circle, first I did the test driving in the room. Then I watched the replays and paused at certain moments. I then took a screenshot of my whole screen, makign sure I was always in 8x zoom. Then I took those screenshots into paint and measured the circle diameter in pixels. I will now describe the process and results of my investigation. But if you dont want to read that, scroll down tot he conclusion on the bottom. Disclaimer: the following formulas are NOT what WG uses, I made a linear model that describes the size of the aimingcircle as close as possible. Aiming circle bloom I assumed there where 3 variables that had an influence on bloom: speed, dispersion and accuray. I tried to do test in which I held 2 variables constant to see the influence of 1. I started with gathering data of 2 different dispersion numbers for which I picked 4 tanks with different accuracy and measured the size at each speedincrease of 10 untill 50 kph. These are the raw results: From that I made a graph of the dispersion in function of speed , and calculated the gradient of the graph assuming linear increase. Then obviously the aiming circle size = C*v+accuracy. With V=speed and C being the gradient, which consist of unknown factors. To check the linear approach was decent I plotted the model and experiment: As you can see the linear approach to the speed factor isnt perfect but not massivly different, only in the middle it differs. I am happy enough with this. Now we need to determine what the C factor consist off. Since there are only 2 variables left, it has to consist dispersion or/and accuracy components. As you can see in the data, with the same dispersion numbers, the aiming circle fort he same speed is bigger when the accuracy is bigger. So there has to be an accuracy factor in C, which is proportional to accuracy. Here you can see accuracy vs circle size: As you can see, the increase isnt marginal. We can now rewrite our formula as: Size=Acc(D*v+1) With D an unknown factor containing dispersion in some form. As we can see, size of aiming circle is directly proportional to accuracy. So an increase in accuracy of 25% will results in 25% better gun handling. This is why the E50/E50M have such amazing gun handling , their dispersion isnt great , but good, but due to the very good accuracy their gun handling is much better than at first glance. The WZ-132-1 has the exact same dispersion values, so you would think the gun handling would bet he same, but no, since it has 33% worse accuracy is will have 33% worse gun handling, which is massive! Thats more than a vstab! Next task is determining the factor D. The only variable left is dispersion, so I tested different tanks with differnt dispersion at the same speed, their accuracy was different, but thats fine, sicne we can normalise for that. These numbers showed that the factor D was proportional to the dispersion values, so D=c*dispersion, with c an unknow constant. Now the formula looks like this: S=Acc(c*d*v+1) Determining c was done by plottign the experminetal result and trying some numbers until the model best fits the experiment. I took c=0.68. The influence of dispersion can be see in this graph: Now we have a formula that gives a perfect description of aiming circle size in function of all variables. Next up is determing a the time it takes fort he circle to shrink, or the actuall aiming time for the tank. Aiming time: We know aiming time is the time it takes fort he circle to shrink by 60% its startign size. So we can write: S1=S2*(4/10)^(t/T) with T=aiming time, S1 size after time t, S2= starting size. Solving this for t we get: t=T*(log(S1/S2)/log(4/10)). We can now determine the time it take from any speed to reach any size we want. To determe the time it takes to fully aim, jsut replace S1 by the accuracy of the gun. Note this time is independant of accuracy! ( which is logical, since it needs to go to a smaller circle but also does it faster, these 2 cancel out) Plotting this for 3 different tank in fucntion of time comming to a stop from a speed of 50 (40 for conway) we get: Influence of equipment/skills etc. Now that we have every formula we need we can quantify the influence of equipment/skills/directives/modules. To do so simply multiply the variable that gets influenced by (1-0,01*improvement in %). Dispersion values only get influenced by vstabs and the smooth ride skill.Other equipment only influences the accuracy value. Note that the same improvement to acc or dispersion results in a bigger improvement in size for what improves acc than what improves dispersion. Vstabs for example do not make the size of the circle shrink by 20%, they make the increase in size less by 20%. Lets take a look at a common dillema:vstabs vs gun laying drive, lets try this on 2 different tanks: We can clearly see what the difference in vstab and gld is, vstab makes the circle smaller, so you start smaller but the decrease is still the same, gld starts at a bigger size but then starts to decrease faster, catching up tot the vstabs. In the BCs case, the time to fully aim is actually lower when equiping gld than when equiping vstabs. Mathmaticly, gld decrease the total time to aim by 10%, whereas vstabs decrease the total time to aim by subtracting 20% *initial size. To know wether vstabs or gld is better depends on the tank and how much you want to aim, you can determine this by pluggin in the numbers and plotting it for each vehicle, sicne i twill be different for each. As general rules however, these apply: · - Bad dispersion + bad aimtime: Vstab better, unless you fully aim from full speed. · - Bad dispersion + good aimtime :Vstab better, unless at high speed when fully aiming. · -Good dispersion + bad aimtime :Vstabs always superior · -Good aimtime + good dispersion :Vstabs always superior Conclusion and TLDR: · - Accuracy has a massive influence on aiming circle size on the move, they are proportional. · - Aiming circle size is proportional to speed/dispersion. · -To determine what gun has better actual gun handling: multply accuracy with dispersion, the lower the numbers the better the gun handling. · - Size of aiming circle= Acc(0.68*d*v+1) · - Time to fully aim = Aiming time*(-log(0.68*d*v+1)/log(4/10)) · - Vstabs is superior to gld in most situations. · - Influencing accuracy gives a better boost than influencing dispersion values. Whats next? Next up I need to investigate how turning the turret and hull effect dipsersion and work with the above formulas. I wil also try to combine this with my previous thread where I determined shot distribution in the aiming circle, then I can plot change to hit a target vs time and determine the optimal time to shoot. I hope you enjoyed the read and that i twill help you determinign how a tank will perform. I hope that youtubers do become aware that accuracy has a massive influence over dispersion, as currently reviews are misleading since they dont know what actually effects gun handling. Spread the word!
Current July/01/20 So here's the post about accuracy. most of this is in bits and pieces from other spots so I'm gathering it all here and adding some new info etc. Have at it! A quick note on dispersion: after turning for 1 second you have reached max hull dispersion and will carry that value until the turn rate is decreased or stopped. Lets knock the nerdy parts out first... The Math There are three factors affecting overall dispersion. One due to moving traverse (affected by Smooth Ride and Vstab), one due to hull traverse (affected by Clutch for the worse, Vstab for the better), and one due to turret traverse (affected by Snap Shot and Vstab), and the files you can verify it in is: res/scripts/avatar.pyc it's unencrypted but you do need a tool reader to view it. Also the lang is python if its not obvious. Some people are reporting this as being encrypted. WG uses the Blowfish cipher, and its not too hard to break. Accuracy and Dispersion Gun Accuracy The accuracy value for a gun is given in meters at a range of 100m. The lower the value the more accurate your gun is. The value describes 2 standard deviations σ from the center of your aim. In other words, for a gun with 0.32m dispersion at 100m, 95.45% of all shots will land within 0.32m of the center of your aim at that distance. Dispersion amount increases linearly with distance, i.e. 0.32m effective accuracy at 100m translates to 0.64m at 200m and 1.28m at 400m. But wait, it gets dumber! Aim time variables confirmed by WG Devs: original radius * (1/e)^(time passed/aim time) or 36.39% per tick of the previous value. not 33/66% or 60/40% because that makes too much damn sense Aiming Circle Sigma Deviations (Picture sauce Thanks Mwtoews ) WG uses a 2 Sigma system now (post 0.8.6) rather than the 3 sigma from before The aiming circle (or reticle/thing that goes on the Red tanks...) describes the area of 2 standard deviations (2σ) from your aim point. Based on a standard normal distribution, this used to mean that 4.2% of your shots would fall outside of the aiming circle. Since version 0.8.6 (the sigma rework) any shots falling outside the 2 Sigma circle get a second roll with a flat distribution (pancake) to place them randomly within the circle (prior to this they were placed on the perimeter). Because of this the shots move (deviate) away from your aim point, outwards toward the edge of the circle, but never shoot past its edge. (the above partially shameless stolen referenced from the wiki. Thanks Haswell ) Equipment Gun Laying Drive vs Vertical Stabilizer Always always always Vert stab. 20% against ALL movement penalties. This means smaller bloom on turret moving, smaller bloom on hull rotation, smaller bloom on the move, Smaller chance of a miss overall. If you aren't running a Vert stab, it should be that you can't equip one. ALL scouts/lights can carry a Vstab now so there's no excuse. Self explanatory chart why start at 1.7x when you can start at 1.27x? It's a much tighter reticle and you still beat the GLD to minimum bloom by .3 sec? Obviously both are best but Rammer - Vstab - Optics are the Trifecta. Vertical Stabilizer +20% to Accuracy during all Movement (AWSD) and Turret rotation (and ALL accuracy it turns out, even stationary, confirmed by WG devs) Gun Laying Drive 10% faster aim in! Generally only useful for snipers and arty. To be used only if a Vstab isn't available AND you are planning to playing a non-peek-a-boom style. Generally not for heavies but sometimes, its what's there. Vents 5% (3.7% effective) better everything, even general crew skills (but not job specific ones) FOOD! A Flat +10% (7.2% effective) to ALL Major Qualifications AND skills/Perks, a huge help in gun Handling and general tank performance Skills As long as you keep moving anything, the bloom continues to bloom, the skills and equipment help to counter the bloom growth. Vents, Vstab and BIA help to actively minimize the bloom dispersion values DURING turning and after as well, everything else just counters the bloom afterwards. BIA: always useful, +5% to general crew skills and to major qualifications, but not to, say Recon or Snapshot) Requires ALL crew members to have it. It's a perk so its 100% effective only (also a good reason to train it 2nd or 3rd). The boost to the Gunner Qualification helps to minimize the bloom penalties by 2.5% effective. Gunner Snap Shot: Pretty useful for all tanks, even casemates and arty. Reduces bloom by 7.5% on turret rotation/Gun movement (3.5 effective). Works great with Vstab! Does stack with Driver's Smooth Ride skill Driver:Clutch braking: Tiny bit faster deg/sec PIVOT turning (A/D only, not W/S) than Off Road, but worse passibility all over. Good for casemates/arty and slow turning tanks (T67 hellcat, grille, T95 etc) This skill can affect Hull turn dispersion by making it worse/faster for a shorter period of time. Nothing makes it better save Vstab/BIA. Clutch Braking is still vital for tactical movement so it's validity isn't questioned but knowledge that it can make your dispersion worse while turning (A/D keys) should be paid attention to. Hull traverse google doc: https://docs.google.com/spreadsheets/d/10VIumnYWrLsc2xpPFnZp-MaVdfBHg_xZOHb04ie1HU8/edit?usp=sharing interesting if you want the raw numbers and why people are all Off Road > Clutch for non-casemates. Smooth Ride: This skill is hotly debated. If your tank has more than .25-.27 dispersion on Forward movement (W key only), it's worth getting early. otherwise, its only use is to counter Clutch Braking's increased dispersion so you should train both this skill and Clutch at the same time to maintain current dispersion values. (more deg/s = more bloom) get if after ORD and Clutch. Look up your favorite tank at Tanks.gg in the stats or compare tabs! @8_Hussars and my work on SR/Snap/Clutch Dispersion values: https://docs.google.com/spreadsheets/d/1TqvlcnQIdPpAzy3X0OK4lxdNjWoqo9ejcdRqu_HqIuc/edit?usp=sharing .25 movement dispersion (which is fairly high) seems to be the 'useful' line for where SR is viable. save for sub tier 6 (and the scout/heavies of 6, not the meds generally) SR should be reserved for a 4th/5th skill. certain premium tanks (type 64, superP) benefit from having the skill but most won't see any kind of useful gain. For the math phobic: based on the work here and the original threads plus some WG dev confirmations since added here, and here:
Hello WoTlabs, Most of my statistics background has been studying distributions such as the normal curve, something that can be applied to game mechanics such as shot penetration and damage. I get lost at the accuracy values. While I understand that a lower value=more accurate (and that's all a player really needs to know), my statistical interest is piqued. How does that value relate to the mathematics side? How many sigma are involved in the accuracy equation? And how are the mechanics for where a shot lands in your reticle calculated? Thanks for your statistical/mathematical expertise.
Since we recently saw a lot of threads comparing the 112, Wz111, the KV-5 and the IS-6 in the current Meta I was quite surprised that most of those threads simply ignored the Given that all four of these tanks sport rather inaccurate guns according to their stats and specifically since the accuracy nerf seems to be mostly aimed at the 122mm Sniper gun three of them carry I though it is necessary to compare those tanks under the light of this change since premium tanks are a long term investment into WoT. Note however that all my knowledge of any tank other than the IS-6 is derived from guides, WoTLabs posts and friends since I don't own them. Thus I would really appreciate it if a tanks owner might post how he thinks his machine will fare if it hits less as all I can do is make a quick guess according to what I read here. So assuming that the planned accuracy nerf hits (even if we don't know much about it) which tank do you think will be hit the least/benefit the most?